Question: Solve for $x$ : $5\sqrt{x} - 3 = 3\sqrt{x} + 10$
Solution: Subtract $3\sqrt{x}$ from both sides: $(5\sqrt{x} - 3) - 3\sqrt{x} = (3\sqrt{x} + 10) - 3\sqrt{x}$ $2\sqrt{x} - 3 = 10$ Add $3$ to both sides: $(2\sqrt{x} - 3) + 3 = 10 + 3$ $2\sqrt{x} = 13$ Divide both sides by $2$ $\frac{2\sqrt{x}}{2} = \frac{13}{2}$ Simplify. $\sqrt{x} = \dfrac{13}{2}$ Square both sides. $\sqrt{x} \cdot \sqrt{x} = \dfrac{13}{2} \cdot \dfrac{13}{2}$ $x = \dfrac{169}{4}$